Eigenstate Thermalization in Dual Unitary Quantum Circuits

• Applicant: Dr. Felix Fritzsch
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 453812159

• Final Report Year: 2024

Final Report Abstract

Fundamental properties of condensed-matter systems as well as the utility of quantum computers emerge from the interaction of a large number of individual particles. As the detailed description of all those individual constituents becomes exponentially more complex with the number of particles growing, an effective description using only a few relevant macroscopic variables is of uttermost importance. While the language of equilibrium statistical physics and thermodynamics provides such an description, it remains a hard problem to justify such a macroscopic equilibrium description from microscopic dynamics and out-of-equilibrium initial conditions. In recent years, the eigenstate thermalization hypothesis has been established as a possible solution to the latter challenge, which has been confirmed in many experimental and numerical studies and which is backed by sound theoretical considerations. A proper mathematical justification, revealing the underlying microscopic mechanism and proving the hypothesis, however, has been missing so far to large extent and was the main objective of this project. More precisely, the hypothesis combines the energy dependence of physical (measurable) observables with statistical properties of stationary energy-eigenstates and their associated energy levels, which turn out to follow the expected behavior derived from the eigenstate thermalization hypothesis and from random-matrix theory. A second main pillar of the project is the efficient and exact computation of the dynamics of the spreading of correlations and quantum information in such circuit models, which allows for explicitly deriving the conjectured statistical properties of physical observables in relation to the energy-eigenstates. Despite their abstract nature, the methods used to obtain such exact results often provide an intuitive explanation for the observed many-body effects based on single- and few-particle properties. Moreover, the findings of this project sparked initial investigations on a more general version of the eigenstate thermalization hypothesis which captures correlations beyond the standard hypothesis and which is conjectured to fully encode the dynamics in chaotic many-body quantum systems. These preliminary findings point towards novel and exciting directions for future research and towards extending the results and the methods of this project.

Publications

• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions. Physical Review E, 103(6).
  Fritzsch, Felix & Prosen, Tomaž
  
• Boundary chaos. Physical Review E, 106(1).
  Fritzsch, Felix & Prosen, Tomaž
  
• Boundary chaos: Exact entanglement dynamics. SciPost Physics, 15(3).
  Fritzsch, Felix; Ghosh, Roopayan & Prosen, Tomaž
  
• Boundary chaos: Spectral form factor. SciPost Physics, 17(5).
  Fritzsch, Felix & Prosen, Tomaž
  
• Universal spectral correlations in interacting chaotic few-body quantum systems. Physical Review E, 109(1).
  Fritzsch, Felix & Kieler, Maximilian F. I.
  
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems. Physical Review Letters, 134(14).
  Pappalardi, Silvia; Fritzsch, Felix & Prosen, Tomaž